My house was built in 1979 and they used trusses instead of floor joices. I was going to strap the trusses and sheetrock. My concern is will the trusses move around as the floor load changes an crack the sheetrock joints?

If you are talking- floor trusses, they won't move that much. Especially with another wall under them, shortening the span. The deflection is rated for loads it could carry, I doubt it is over-spanned for the application as these require engineering before installation.